If the source of light is on opposite end of diameter, the resultant projection will be:

Question

Accepted Answer

The correct answer is Option 2: Stereographic. Here's why:

**Why Stereographic Projection is Correct:**

Stereographic projection is defined as a projection where the projection point (the light source in this case) is located on the surface of the sphere, *opposite* the point where the plane of projection is tangent to the sphere. Specifically, if the plane of projection is tangent at the South Pole, the light source (projection point) is at the North Pole (or vice versa). This perfectly matches the description in the question: "the source of light is on opposite end of diameter."

The key characteristic of stereographic projection is that it preserves angles locally (it's conformal). While it distorts area and shape, the angles between features are maintained at a point. This makes it useful for applications where angular relationships are important, such as navigation and mapping of small areas. The question describes the *geometry* of the projection setup, and stereographic projection is the only one that fits that geometry precisely.

**Why the Other Options are Incorrect:**

*   **Option 1: Gnomonic:** Gnomonic projection has the projection point at the *center* of the sphere. This is fundamentally different from the question's description of the light source being at the opposite end of the diameter. Gnomonic projections are known for projecting great circles as straight lines, but they severely distort shape and area, especially away from the center of the projection.

*   **Option 3: Orthomorphic:** Orthomorphic is a *property* of a projection, meaning it preserves angles locally (conformal). While stereographic projection *is* orthomorphic, the term "orthomorphic" itself doesn't define a specific projection method or the location of the light source. The question asks for the *type* of projection based on the light source's location, not a property of the projection. Therefore, while related, it's not the most accurate answer.

*   **Option 4: Orthographic:** Orthographic projection has the projection point at infinity. This means the light rays are parallel and perpendicular to the projection plane. This is completely different from the question's description of the light source being at the opposite end of the diameter. Orthographic projections are often used to show true shapes and sizes of objects when viewed from a specific direction, but they don't fit the described geometry.